@article{KoflerWaldKolbitschetal.2024, author = {Kofler, Andreas and Wald, Christian and Kolbitsch, Christoph and von Tycowicz, Christoph and Ambellan, Felix}, title = {Joint Reconstruction and Segmentation in Undersampled 3D Knee MRI combining Shape Knowledge and Deep Learning}, volume = {69}, journal = {Physics in Medicine and Biology}, number = {9}, doi = {10.1088/1361-6560/ad3797}, year = {2024}, abstract = {Task-adapted image reconstruction methods using end-to-end trainable neural networks (NNs) have been proposed to optimize reconstruction for subsequent processing tasks, such as segmentation. However, their training typically requires considerable hardware resources and thus, only relatively simple building blocks, e.g. U-Nets, are typically used, which, albeit powerful, do not integrate model-specific knowledge. In this work, we extend an end-to-end trainable task-adapted image reconstruction method for a clinically realistic reconstruction and segmentation problem of bone and cartilage in 3D knee MRI by incorporating statistical shape models (SSMs). The SSMs model the prior information and help to regularize the segmentation maps as a final post-processing step. We compare the proposed method to a state-of-the-art (SOTA) simultaneous multitask learning approach for image reconstruction and segmentation (MTL) and to a complex SSMs-informed segmentation pipeline (SIS). Our experiments show that the combination of joint end-to-end training and SSMs to further regularize the segmentation maps obtained by MTL highly improves the results, especially in terms of mean and maximal surface errors. In particular, we achieve the segmentation quality of SIS and, at the same time, a substantial model reduction that yields a five-fold decimation in model parameters and a computational speedup of an order of magnitude. Remarkably, even for undersampling factors of up to R=8, the obtained segmentation maps are of comparable quality to those obtained by SIS from ground-truth images.}, language = {en} } @article{NavaYazdaniHegeSullivanetal.2020, author = {Nava-Yazdani, Esfandiar and Hege, Hans-Christian and Sullivan, T. J. and von Tycowicz, Christoph}, title = {Geodesic Analysis in Kendall's Shape Space with Epidemiological Applications}, volume = {62}, journal = {Journal of Mathematical Imaging and Vision}, number = {4}, arxiv = {http://arxiv.org/abs/1906.11950}, doi = {10.1007/s10851-020-00945-w}, pages = {549 -- 559}, year = {2020}, abstract = {We analytically determine Jacobi fields and parallel transports and compute geodesic regression in Kendall's shape space. Using the derived expressions, we can fully leverage the geometry via Riemannian optimization and thereby reduce the computational expense by several orders of magnitude over common, nonlinear constrained approaches. The methodology is demonstrated by performing a longitudinal statistical analysis of epidemiological shape data. As an example application we have chosen 3D shapes of knee bones, reconstructed from image data of the Osteoarthritis Initiative (OAI). Comparing subject groups with incident and developing osteoarthritis versus normal controls, we find clear differences in the temporal development of femur shapes. This paves the way for early prediction of incident knee osteoarthritis, using geometry data alone.}, language = {en} } @article{AmbellanZachowvonTycowicz2021, author = {Ambellan, Felix and Zachow, Stefan and von Tycowicz, Christoph}, title = {Rigid Motion Invariant Statistical Shape Modeling based on Discrete Fundamental Forms}, volume = {73}, journal = {Medical Image Analysis}, arxiv = {http://arxiv.org/abs/2111.06850}, doi = {10.1016/j.media.2021.102178}, year = {2021}, abstract = {We present a novel approach for nonlinear statistical shape modeling that is invariant under Euclidean motion and thus alignment-free. By analyzing metric distortion and curvature of shapes as elements of Lie groups in a consistent Riemannian setting, we construct a framework that reliably handles large deformations. Due to the explicit character of Lie group operations, our non-Euclidean method is very efficient allowing for fast and numerically robust processing. This facilitates Riemannian analysis of large shape populations accessible through longitudinal and multi-site imaging studies providing increased statistical power. Additionally, as planar configurations form a submanifold in shape space, our representation allows for effective estimation of quasi-isometric surfaces flattenings. We evaluate the performance of our model w.r.t. shape-based classification of hippocampus and femur malformations due to Alzheimer's disease and osteoarthritis, respectively. In particular, we achieve state-of-the-art accuracies outperforming the standard Euclidean as well as a recent nonlinear approach especially in presence of sparse training data. To provide insight into the model's ability of capturing biological shape variability, we carry out an analysis of specificity and generalization ability.}, language = {en} } @article{vonTycowiczAmbellanMukhopadhyayetal.2018, author = {von Tycowicz, Christoph and Ambellan, Felix and Mukhopadhyay, Anirban and Zachow, Stefan}, title = {An Efficient Riemannian Statistical Shape Model using Differential Coordinates}, volume = {43}, journal = {Medical Image Analysis}, number = {1}, doi = {10.1016/j.media.2017.09.004}, pages = {1 -- 9}, year = {2018}, abstract = {We propose a novel Riemannian framework for statistical analysis of shapes that is able to account for the nonlinearity in shape variation. By adopting a physical perspective, we introduce a differential representation that puts the local geometric variability into focus. We model these differential coordinates as elements of a Lie group thereby endowing our shape space with a non-Euclidean structure. A key advantage of our framework is that statistics in a manifold shape space becomes numerically tractable improving performance by several orders of magnitude over state-of-the-art. We show that our Riemannian model is well suited for the identification of intra-population variability as well as inter-population differences. In particular, we demonstrate the superiority of the proposed model in experiments on specificity and generalization ability. We further derive a statistical shape descriptor that outperforms the standard Euclidean approach in terms of shape-based classification of morphological disorders.}, language = {en} } @article{OehmeMoewisBoethetal.2024, author = {Oehme, Stephan and Moewis, Philippe and Boeth, Heide and Bartek, Benjamin and von Tycowicz, Christoph and Ehrig, Rainald and Duda, Georg and Jung, Tobias}, title = {Altered knee kinematics after posterior cruciate single-bundle reconstruction - a comprehensive prospective biomechanical in vivo analysis}, volume = {12}, journal = {Frontiers in Bioengineering and Biotechnology}, doi = {10.3389/fbioe.2024.1322136}, year = {2024}, language = {en} } @article{DietrichvonTycowiczBrandletal.2026, author = {Dietrich, Laura and von Tycowicz, Christoph and Brandl, Michael and Mayer, Julius and Baunack, Lohengrin and Schmidt, Iris}, title = {Project WEAR: Developing a methodological framework for functional analysis on stone tools through controlled experiments and computational modelling of shape transformations through use}, journal = {Antiquity}, year = {2026}, abstract = {The WEAR project is developing an integrative methodology to analyse and predict use-related shape transformation of Neolithic stone axes from Central Europe with mathematical methods and experimental archaeology.}, language = {en} } @article{VeldhuijzenVeltkampIkneetal.2024, author = {Veldhuijzen, Ben and Veltkamp, Remco C. and Ikne, Omar and Allaert, Benjamin and Wannous, Hazem and Emporio, Marco and Giachetti, Andrea and LaViola Jr, Joseph J. and He, Ruiwen and Benhabiles, Halim and Cabani, Adnane and Fleury, Anthony and Hammoudi, Karim and Gavalas, Konstantinos and Vlachos, Christoforos and Papanikolaou, Athanasios and Romanelis, Ioannis and Fotis, Vlassis and Arvanitis, Gerasimos and Moustakas, Konstantinos and Hanik, Martin and Nava-Yazdani, Esfandiar and von Tycowicz, Christoph}, title = {SHREC 2024: Recognition Of Dynamic Hand Motions Molding Clay}, volume = {123}, journal = {Computers \& Graphics}, doi = {10.1016/j.cag.2024.104012}, pages = {104012}, year = {2024}, abstract = {Gesture recognition is a tool to enable novel interactions with different techniques and applications, like Mixed Reality and Virtual Reality environments. With all the recent advancements in gesture recognition from skeletal data, it is still unclear how well state-of- the-art techniques perform in a scenario using precise motions with two hands. This paper presents the results of the SHREC 2024 contest organized to evaluate methods for their recognition of highly similar hand motions using the skeletal spatial coordinate data of both hands. The task is the recognition of 7 motion classes given their spatial coordinates in a frame-by-frame motion. The skeletal data has been captured using a Vicon system and pre-processed into a coordinate system using Blender and Vicon Shogun Post. We created a small, novel dataset with a high variety of durations in frames. This paper shows the results of the contest, showing the techniques created by the 5 research groups on this challenging task and comparing them to our baseline method.}, language = {en} } @article{MayerBaumAmbellanetal.2024, author = {Mayer, Julius and Baum, Daniel and Ambellan, Felix and von Tycowicz, Christoph and for the Alzheimer's Disease Neuroimaging Initiative,}, title = {Shape-based Disease Grading via Functional Maps and Graph Convolutional Networks with Application to Alzheimer's Disease}, volume = {24}, journal = {BMC Medical Imaging}, doi = {10.1186/s12880-024-01513-z}, year = {2024}, abstract = {Shape analysis provides methods for understanding anatomical structures extracted from medical images. However, the underlying notions of shape spaces that are frequently employed come with strict assumptions prohibiting the analysis of incomplete and/or topologically varying shapes. This work aims to alleviate these limitations by adapting the concept of functional maps. Further, we present a graph-based learning approach for morphometric classification of disease states that uses novel shape descriptors based on this concept. We demonstrate the performance of the derived classifier on the open-access ADNI database differentiating normal controls and subjects with Alzheimer's disease. Notably, the experiments show that our approach can improve over state-of-the-art from geometric deep learning.}, language = {en} } @article{HanikDuckeHegeetal.2023, author = {Hanik, Martin and Ducke, Benjamin and Hege, Hans-Christian and Fless, Friederike and von Tycowicz, Christoph}, title = {Intrinsic shape analysis in archaeology: A case study on ancient sundials}, volume = {16}, journal = {Journal on Computing and Cultural Heritage}, number = {4}, arxiv = {http://arxiv.org/abs/2305.18960}, doi = {10.1145/3606698}, pages = {1 -- 26}, year = {2023}, abstract = {The fact that the physical shapes of man-made objects are subject to overlapping influences—such as technological, economic, geographic, and stylistic progressions—holds great information potential. On the other hand, it is also a major analytical challenge to uncover these overlapping trends and to disentagle them in an unbiased way. This paper explores a novel mathematical approach to extract archaeological insights from ensembles of similar artifact shapes. We show that by considering all shape information in a find collection, it is possible to identify shape patterns that would be difficult to discern by considering the artifacts individually or by classifying shapes into predefined archaeological types and analyzing the associated distinguishing characteristics. Recently, series of high-resolution digital representations of artifacts have become available. Such data sets enable the application of extremely sensitive and flexible methods of shape analysis. We explore this potential on a set of 3D models of ancient Greek and Roman sundials, with the aim of providing alternatives to the traditional archaeological method of "trend extraction by ordination" (typology). In the proposed approach, each 3D shape is represented as a point in a shape space—a high-dimensional, curved, non-Euclidean space. Proper consideration of its mathematical properties reduces bias in data analysis and thus improves analytical power. By performing regression in shape space, we find that for Roman sundials, the bend of the shadow-receiving surface of the sundials changes with the latitude of the location. This suggests that, apart from the inscribed hour lines, also a sundial's shape was adjusted to the place of installation. As an example of more advanced inference, we use the identified trend to infer the latitude at which a sundial, whose location of installation is unknown, was placed. We also derive a novel method for differentiated morphological trend assertion, building upon and extending the theory of geometric statistics and shape analysis. Specifically, we present a regression-based method for statistical normalization of shapes that serves as a means of disentangling parameter-dependent effects (trends) and unexplained variability. In addition, we show that this approach is robust to noise in the digital reconstructions of the artifact shapes.}, language = {en} } @article{OehmeMoewisBoethetal.2022, author = {Oehme, Stephan and Moewis, Philippe and Boeth, Heide and Bartek, Benjamin and Lippert, Annika and von Tycowicz, Christoph and Ehrig, Rainald and Duda, Georg and Jung, Tobias}, title = {PCL insufficient patients with increased translational and rotational passive knee joint laxity have no increased range of anterior-posterior and rotational tibiofemoral motion during level walking}, volume = {12}, journal = {Scientific Reports}, number = {1}, doi = {10.1038/s41598-022-17328-3}, pages = {1 -- 11}, year = {2022}, language = {en} }